The sun gets the ball rolling. Does it mean solar panels stop generating electricity as dusk falls, and get back to work at the crack of dawn? Well, it's true that the sun doesn't shine at night. However, some experts believe that moonlight can also power PV cells, so panels might produce around 10 W a night. It will be enough to boil the kettle or keep the light on in the bathroom all night. Even if those experts are wrong, you can always go for some cost-effective battery solutions to store the energy you have harvested during the day. There is no such thing as a minimal setup though. Your options range from relatively simple solutions like KiloVault PLC 2100 to all-in-one storage systems like Enphase Encharge 10.
As for clouds, rain, snow and other precipitations, they do decrease the solar panel's efficiency, but only by around 10-25%. While they are capable of blocking direct sunlight, solar radiation in different ranges of wavelength still penetrates solar panels. It means electricity generation continues whatever the weather. Read How solar panels perform on cloudy days and why electricity prices matter more than the weather
to find out how solar panels perform under different conditions.